I have installed SQL Server Express 2008 R2 Express version and have created various tables and stored procedures. I start Reporting Services Configuration Manager, connect to my report server instance, click on Report Manager URL and get my SQL Server Reporting Services Home page. I have the “New folder, New Data Source, Folder and Upload buttons, but I do not have a Report Builder button. Can someone tell me what the problem is? Everything else seems to be working except the most important piece, the ability to create a report.

Ok, now I see. 2008 R2 support Reporting Services but according to your link "Ad hoc reporting through semantic models and ReportBuilder is not supported."

It does appear to support report building through "BI Development Studio. This provides an integrated report creation and design environment to create reports."

Would you know if BIDS as it is called, works that same as Report Builder?

BIDS doesnt work same way as report builder. BIDS is much more enhanced tool than report builder.Report builder needs a deployed report model for you to consume and create reports out of it.BIDS doesnt need a deployed model. It can create the metadata by using a defined database connection and dataset which will have query/procedure to get required data. So its much more flexible than report builder.